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What is the image of (1 -6) for a 270 counterclockwise rotation about the origin?
It is (-6, -1).
What is the image of 1 -6 for a 90 counterclockwise rotation about the origin?
(-1, -4) rotated 90 degrees anticlockwise
What is the image of (1 -6) for a 180 counterclockwise rotation about the origin?
It is (-1, 6).Also, if the rotation is 180 degrees, then clockwise or anticlockwise are irrelevant.It is (-1, 6).
What happens to the x and y coordinates when rotating a figure counterclockwise?
A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)
How Translating the point of origin?
Origin is at points (0, 0) in coordinate geometry. If you are shifting/translating the origin, you have to add the respective x and y coordinates of the new origin with respect to the old origin to get the coordinates of the new origin.
What is the image of 1 -6 for a 270 counterclockwise rotation about the origin?
To find the image of the point (1, -6) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The coordinates transform as follows: (x, y) becomes (y, -x). Therefore, the image of (1, -6) is (-6, -1).
What is the image of (1 -6) for a 180 degree counterclockwise rotation about the origin?
To find the image of the point (1, -6) after a 180-degree counterclockwise rotation about the origin, you can use the rotation transformation. A 180-degree rotation changes the coordinates (x, y) to (-x, -y). Therefore, the image of the point (1, -6) is (-1, 6).
What is a rotation of 90 Degrees counterclockwise?
A rotation of 90 degrees counterclockwise is a transformation that turns a point or shape around a fixed point (usually the origin in a coordinate plane) by a quarter turn in the opposite direction of the clock's hands. For a point with coordinates (x, y), this rotation results in new coordinates (-y, x). This type of rotation is commonly used in geometry and computer graphics to manipulate shapes and objects.
What is the image of 1 -6 after a 180 degree counterclockwise rotation about the origin?
A 180° rotation is half a rotation and it doesn't matter if it is clockwise of counter clockwise. When rotating 180° about the origin, the x-coordinate and y-coordinates change sign Thus (1, -6) → (-1, 6) after rotating 180° around the origin.
What is a rotation of 180 Degrees counterclockwise?
A rotation of 180 degrees counterclockwise refers to turning a point or shape around a central point (such as the origin in a coordinate plane) by half a turn. This effectively moves each point to a position that is directly opposite its starting point. For example, if a point is at coordinates (x, y), after a 180-degree counterclockwise rotation, its new coordinates will be (-x, -y). This transformation maintains the shape and size but changes its orientation.
How do you rotate 180 degrees counter clockwise about origin?
To rotate a point 180 degrees counterclockwise about the origin, you can simply change the signs of both the x and y coordinates of the point. For example, if the original point is (x, y), after the rotation, the new coordinates will be (-x, -y). This effectively reflects the point across the origin.
What is image of point 4 3 if rotation is 90?
To find the image of the point (4, 3) after a 90-degree rotation counterclockwise about the origin, you can use the transformation formula for rotation. The new coordinates will be (-y, x), which means the image of the point (4, 3) will be (-3, 4).
What is the image of (1 -6) for a 270 counterclockwise rotation about the origin?
It is (-6, -1).
What is the Rotation rule for 180 counter clockwise?
The rotation rule for a 180-degree counterclockwise rotation involves turning a point around the origin (0, 0) by half a circle. For any point (x, y), the new coordinates after this rotation become (-x, -y). This means that both the x and y coordinates are negated. For example, the point (3, 4) would rotate to (-3, -4).
What is the image of (1 -6) for a 90 and deg counterclockwise rotation about the origin?
It is (-1, 6).
what is the image of the point (-2,7) after a rotation of 180 counterclockwise about the origin?
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
How does the coordinates change in rotation?
When a point ((x, y)) is rotated around the origin by an angle (\theta), the new coordinates ((x', y')) can be determined using the rotation formulas: (x' = x \cos(\theta) - y \sin(\theta)) and (y' = x \sin(\theta) + y \cos(\theta)). This transformation effectively changes the point's position in a circular motion around the origin based on the specified angle. The direction of rotation (clockwise or counterclockwise) also affects the signs of the trigonometric functions used.
